
A chequerboard density filter typically of the form \(f_1(\mathbf {x}) = \mathbf {A} \mathbf {x}\)  for some constant matrix \(\mathbf {A}\)  [1]},

An interpolation of the form \(f_2(y) = (1 - x_{min})y + x_{min}\)  applied element-wise for some small \(x_{min} > 0\)  such as \(0.001\) ,

A penalty such as the power penalty \(f_3(z) = z^p\)  applied element-wise for some penalty value \(p\) , and

A projection method such as the regularized Heaviside projection [2]} applied element-wise.

